October 24 2014: Google has come up with a new email service it's calling Inbox -- and it promises to be a radical departure to what wer're used to.  It is available as an app for the Web, Apple's iOS and Google's own Android operating system, but for now  Inbox is an invitation-only option; Gmail users can request access by sending an email to inbox@google.com. 
We have Google's own explanatory video in our tech video spot on this page -- and append below some highlights gleaned by CNet:

It automatically groups emails into categories called bundles, creating several of its own and letting you add your own.
It lets you easily declare yourself done with individual messages or entire bundles.
It gives messages a snooze button if you want to deal with them later and a pin button to keep important message front and center.
It offers a big round button on the lower right of the screen for quick access to a choice of likely actions.
It spotlights extracts of individual messages and augments them with online information such as airline flight status.